Correlation emergence in two coupled simulated limit order books

TL;DR

This paper models the correlation emergence between two coupled limit order books using a fluid limit approach, demonstrating how the Epps effect can arise from trader interactions without microstructure noise.

Contribution

It introduces a novel fluid limit model of coupled order books that captures correlation effects and the Epps effect through trader interactions and asynchronous events.

Findings

The model reproduces the Epps effect without microstructure noise.

Correlation depends on time and price discretisation choices.

The approach highlights emergent properties from trader interactions.

Abstract

We use random walks to simulate the fluid limit of two coupled diffusive limit order books to model correlation emergence. The model implements the arrival, cancellation and diffusion of orders coupled by a pairs trader profiting from the mean-reversion between the two order books in the fluid limit for a Lit order book with vanishing boundary conditions and order volume conservation. We are able to demonstrate the recovery of an Epps effect from this. We discuss how various stylised facts depend on the model parameters and the numerical scheme and discuss the various strengths and weaknesses of the approach. We demonstrate how the Epps effect depends on different choices of time and price discretisation. This shows how an Epps effect can emerge without recourse to market microstructure noise relative to a latent model but can rather be viewed as an emergent property arising from trader interactions in a world of asynchronous events.